Brazil Stock Market Analysis in R
Caio Moreno
November 17, 2015
In this analysis I used real data from Brazil Stock Market.
I will create a R package called r-stock-analysis https://github.com/caiomsouza/r-stock-analysis
http://www.thertrader.com/2014/02/28/using-cart-for-stock-market-forecasting/
https://cran.r-project.org/web/packages/stocks/index.html
https://www.youtube.com/watch?v=iMET2gbsbHY
http://www.r-chart.com/2010/06/stock-analysis-using-r.html
TAREA 2: Cuantificación del riesgo de Mercado (primera del profesor Escot)
En esta tarea se trata de que apliquéis los métodos mostrados en clase para cuantificar el riesgo de mercado de los activos financieros.
1- Selección de variables: debeis seleccionar 5 valores (acciones) del mercado continuo español más el ibex 35 y bajar la serie completa. Para el punto 2 y 3 se utilizarán las series temporales completas hasta el 30 de septiembre de 2015. el mes de octubre se reservará para hacer predicciones
2.- ¿Son los mercados de estos 6 valores eficientes?
3.- ¿Se puede modelizar la serie de rendimientos diarios de estos valores?. ¿Que modelo predice mejor (utiliazando el error cuadrático medio)?
4.- Utilizando información de los dos últimos años. ¿cual es la mejor cartera que se puede formar con esos 5 valores?. Suponga para ello dos posibilidades, que los agentes son aversos al riesgos y no tienen otras alternativas de inversión (es deseable la cartera de menor riesgo); y en segundo lugar que existe la posibilidad de invertir (o endeudarse) a un tipo de interés sin riesgo del 0.5%. ¿Cómo se comportan estas carteras durante el mes de octubre mejor o peor que el ibex?. ¿Cual es la beta de los 5 valores? ¿y la beta de la cartera?, ¿cual de los cinco valores ha tenido un comportamiento mejor que lo esperado según la teorÃa del CAPM?
- Utilizando información del último año determine el valor en riesgo de su cartera óptima para el dÃa uno de octubre de 2015 suponiendo que posee una riqueza financiera total de 1000 euros que tiene que repartir entre los cinco valores. Repita la estimación del Valor en riesgo para todos los dÃas hábiles del mes de octubre y realice una prueba de estrés y una prueba de comprobación (backtesting) para saber si su estimación del VaR (Value at Risk) es correcta.
Por favor entregue un archivo word o pdf con los resultados principales de su trabajo explicando qué es lo que obtiene y que se deriva de dichos resultados. Puede incluir en el código R en el texto principal o al final del texto en un anexo, se valorará positivamente.
# UCM
# Prof. Lorenzo Escot
# Alumno: Caio Fernandes Moreno (caiofern@ucm.es)
# Brazil Stock Market Analysis
setwd("~/git/Bitbucket/ucm/SCORE/tareas/Lorenzo-Escot")
library(tseries) # adf.test, kpss.test, bds.test, get.hist.quote, portfolio.optim, surrogate, arma, garch
#install.packages("forecast")
library(forecast)## Loading required package: zoo
##
## Attaching package: 'zoo'
##
## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric
##
## Loading required package: timeDate
## This is forecast 6.2# En el paquete forecast tiene un modelo auto ARIMA.
#install.packages("fArma")
library(fArma) #ARMAFIT, RSFIT## Loading required package: timeSeries
##
## Attaching package: 'timeSeries'
##
## The following object is masked from 'package:zoo':
##
## time<-
##
## Loading required package: fBasics
##
##
## Rmetrics Package fBasics
## Analysing Markets and calculating Basic Statistics
## Copyright (C) 2005-2014 Rmetrics Association Zurich
## Educational Software for Financial Engineering and Computational Science
## Rmetrics is free software and comes with ABSOLUTELY NO WARRANTY.
## https://www.rmetrics.org --- Mail to: info@rmetrics.org#install.packages("fGarch")
library(fGarch) #GARCHFIT formula ~arma (2,1) + garch (1,1) # ~ AltGr + 4
#install.packages("outliers")
library(outliers) #: outlier, rm.outlier, scores, chisq.out.test # para detectar outliers o datos an?malos ojo serie estacionaria##
## Attaching package: 'outliers'
##
## The following object is masked from 'package:timeSeries':
##
## outlier#install.packages("zoo")
library(zoo)
#setinternet2() #esto abre el puerto de internet
#stock.name <- "^BVSP"
#stock.description <- "IBOVESPA"
generateAnalysis <- function(x, y) {
stock.name <- x
stock.description <- y
## lectura de los datos hist?ricos del ^BVSP
stock.name <- get.hist.quote(instrument=stock.name, quote="AdjClose")
# BVSP time series starts 1993-04-27
# http://finance.yahoo.com/q?s=%5EBVSP
series.name <- stock.name
str(series.name)
summary(series.name)
start(series.name)
end(series.name)
plot(series.name)
head(series.name, 10)
tail(series.name, 10)
# Mirando los datos he decidido con la ayuda del Prof. Lorenzo no quitar los datos de 1993 hasta 1998.
#?existen datos nulos?
length(series.name)
length(series.name[!is.na(series.name)])
length(complete.cases(series.name))
#parece que no, pero si tuviera na se podr?an quitar con: ibex<-ibex[complete.cases(ibex)]
series.name<-series.name[complete.cases(series.name)]
plot(series.name)
### podemos seleccionar una submuestra: Temporal
series.name.short <-window(series.name,start=as.Date("1993-04-27"),end=as.Date("2015-09-30"))
str(series.name.short)
summary(series.name.short)
plot(series.name.short)
## Calculo la serie de rendimientos
d.series.name <- diff(log(series.name.short))
# Concatenate stock.description with the text Withall
plot.description <- paste(stock.description, "WITH ALL DATA", collapse = ", ")
#Grafico de la serie
plot(d.series.name, main=(plot.description))
#Datos an?malos
# type = z Busca los datos tipificados mayor que 5 vezes la sd (disviacion tipica)
# Remove datos anomalos
remove.outlier.d.series.name <- d.series.name[abs(scores(d.series.name, type="z"))<=5]
#plot(remove.outlier.d.series.name, main="IBOVESPA WITHOUT OUTLIERS")
# Concatenate stock.description with the text Withall
plot.description <- paste(stock.description, " WITHOUT OUTLIERS", collapse = ", ")
#Grafico de la serie
plot(d.series.name, main=(plot.description))
#?es estacionario?
adf.test(d.series.name)# Ho: una ra?z unitaria (no estacionaria)
# Augmented Dickey-Fuller Test
# data: dBVSP
# Dickey-Fuller = -14.073, Lag order = 17, p-value = 0.01
# alternative hypothesis: stationary
# No es estacionaria
sd(d.series.name) #desviaci?n t?pica
# Statistical stationarity:
# http://people.duke.edu/~rnau/411diff.htm
#?presenta correlaci?n?
df.d.series.name <- as.data.frame(d.series.name)
#periodograma
par(mfrow=c(2,1))
acf(df.d.series.name, ylim=c(-1,1))
pacf(df.d.series.name, ylim=c(-1,1))
tsdisplay(df.d.series.name)
# test bds
bds.test(d.series.name,m=10) # H0: i.i.d
#test R/, exponente de Hurst
HURST<-rsFit(d.series.name, doplot = T)# Exponente de Hurst 0.5 ruido blanco
HURST
##Se puede hacer el test de Hurst=0.5 con el siguiente estad?stico t ##
t<-(HURST@hurst$diag[2,1]-0.5)/HURST@hurst$diag[2,2]
t
#Modelo Auto Arima
modelo.auto.arima <- auto.arima(d.series.name)
plot(forecast(modelo.auto.arima,h=20))
modelo.auto.arima1 <- auto.arima(d.series.name)
plot(forecast(modelo.auto.arima1, h=1))
# alternativa
d.series.name.ARMA<-armaFit(~ arma(1,3), data=d.series.name)
summary(d.series.name.ARMA, wich="all")
residuo<-residuals(d.series.name.ARMA)
plot(residuo)
lines(residuo)
df.residuo <- as.data.frame(residuo)
#periodograma
par(mfrow=c(2,1))
acf(df.residuo, ylim=c(-1,1))
pacf(df.residuo, ylim=c(-1,1))
#x11()
tsdisplay(df.residuo)
# test bds
bds.test(d.series.name,m=10) # H0: i.i.d
#test R/, exponente de Hurst
HURST<-rsFit(d.series.name, doplot = T)# Exponente de Hurst 0.5 ruido blanco
HURST
# Este codigo ha tenido muchas modificaciones hay que cojer el codigo del profesor Lorenzo.
##Se puede hacer el test de Hurst=0.5 con el siguiente estad?stico t ##
t<-(HURST@hurst$diag[2,1]-0.5)/HURST@hurst$diag[2,2]
t
####PREDICCIONES
predict(d.series.name.ARMA, n.ahead=10, conf=c(90,95), dplot=True)
#alternativo
d.series.name.ARMAGARCH<-garchFit(~ arma(1,1) + garch(2,1), data=d.series.name, include.mean=TRUE) ####aqu? el orden es GARCH,ARCH
summary(d.series.name.ARMAGARCH)
plot(d.series.name.ARMAGARCH@residuals)
residuogarch<-residuals(d.series.name.ARMAGARCH)
volatilitygarch<-volatility(d.series.name.ARMAGARCH)
plot(volatilitygarch)
lines(volatilitygarch)
plot(d.series.name^2)
predict(d.series.name.ARMAGARCH, n.ahead=10, conf=c(90,95), dplot=TRUE)
}
# IBOVESPA
stock.name <- "^BVSP"
stock.description <- "IBOVESPA"
# Call your function and pass x and y to the function
run <- generateAnalysis(stock.name,stock.description)## time series starts 1993-04-27
## 'zoo' series from 1993-04-27 to 2016-01-06
## Data: num [1:5635, 1] 24.5 24.3 23.7 24.1 24.1 ...
## - attr(*, "dimnames")=List of 2
## ..$ : NULL
## ..$ : chr "AdjClose"
## Index: Date[1:5635], format: "1993-04-27" "1993-04-28" "1993-04-29" "1993-04-30" ...
## 'zoo' series from 1993-04-27 to 2015-09-30
## Data: num [1:5572] 24.5 24.3 23.7 24.1 24.1 ...
## Index: Date[1:5572], format: "1993-04-27" "1993-04-28" "1993-04-29" "1993-04-30" ...
## Warning in adf.test(d.series.name): p-value smaller than printed p-value
## Warning in sqrt(diag(fit$var.coef)): NaNs produced
##
## Title:
## ARIMA Modelling
##
## Call:
## armaFit(formula = ~arma(1, 3), data = d.series.name)
##
## Model:
## ARIMA(1,0,3) with method: CSS-ML
##
## Coefficient(s):
## ar1 ma1 ma2 ma3 intercept
## 0.028451 0.027562 -0.006066 -0.012289 0.001349
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.1724656 -0.0116332 -0.0002197 0.0116098 0.2916280
##
## Moments:
## Skewness Kurtosis
## 0.5518 10.4767
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## ar1 0.0284509 NA NA NA
## ma1 0.0275620 NA NA NA
## ma2 -0.0060665 NA NA NA
## ma3 -0.0122894 0.0034857 -3.526 0.000422 ***
## intercept 0.0013495 0.0003251 4.151 3.31e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## sigma^2 estimated as: 0.0005446
## log likelihood: 13029.24
## AIC Criterion: -26046.48
##
## Description:
## Thu Jan 7 16:12:14 2016 by user:
##
## Series Initialization:
## ARMA Model: arma
## Formula Mean: ~ arma(1, 1)
## GARCH Model: garch
## Formula Variance: ~ garch(2, 1)
## ARMA Order: 1 1
## Max ARMA Order: 1
## GARCH Order: 2 1
## Max GARCH Order: 2
## Maximum Order: 2
## Conditional Dist: norm
## h.start: 3
## llh.start: 1
## Length of Series: 5571
## Recursion Init: mci
## Series Scale: 0.02337828
##
## Parameter Initialization:
## Initial Parameters: $params
## Limits of Transformations: $U, $V
## Which Parameters are Fixed? $includes
## Parameter Matrix:
## U V params includes
## mu -0.57716768 0.5771677 0.05772286 TRUE
## ar1 -0.99999999 1.0000000 -0.04584008 TRUE
## ma1 -0.99999999 1.0000000 0.10215077 TRUE
## omega 0.00000100 100.0000000 0.10000000 TRUE
## alpha1 0.00000001 1.0000000 0.05000000 TRUE
## alpha2 0.00000001 1.0000000 0.05000000 TRUE
## gamma1 -0.99999999 1.0000000 0.10000000 FALSE
## gamma2 -0.99999999 1.0000000 0.10000000 FALSE
## beta1 0.00000001 1.0000000 0.80000000 TRUE
## delta 0.00000000 2.0000000 2.00000000 FALSE
## skew 0.10000000 10.0000000 1.00000000 FALSE
## shape 1.00000000 10.0000000 4.00000000 FALSE
## Index List of Parameters to be Optimized:
## mu ar1 ma1 omega alpha1 alpha2 beta1
## 1 2 3 4 5 6 9
## Persistence: 0.9
##
##
## --- START OF TRACE ---
## Selected Algorithm: nlminb
##
## R coded nlminb Solver:
##
## 0: 7007.5070: 0.0577229 -0.0458401 0.102151 0.100000 0.0500000 0.0500000 0.800000
## 1: 6912.5211: 0.0577222 -0.0462831 0.101731 0.0745310 0.0495072 0.0487042 0.786314
## 2: 6853.3005: 0.0577207 -0.0470350 0.101025 0.0634282 0.0685389 0.0667259 0.791504
## 3: 6836.3228: 0.0577203 -0.0472069 0.100865 0.0568509 0.0683983 0.0664953 0.789530
## 4: 6820.2471: 0.0577188 -0.0477502 0.100360 0.0438816 0.0716566 0.0695678 0.788959
## 5: 6812.6945: 0.0577096 -0.0502291 0.0980834 0.0378664 0.0817180 0.0812599 0.810664
## 6: 6805.5983: 0.0576893 -0.0540431 0.0946779 0.0164254 0.0748376 0.0771232 0.825021
## 7: 6794.9712: 0.0575556 -0.0718150 0.0795594 0.0237874 0.0753770 0.0716922 0.836102
## 8: 6788.5061: 0.0574791 -0.0557498 0.0969688 0.0199860 0.0745192 0.0629286 0.846183
## 9: 6787.9674: 0.0574787 -0.0557881 0.0969381 0.0190952 0.0740933 0.0624548 0.845810
## 10: 6787.5205: 0.0574688 -0.0566813 0.0962259 0.0199000 0.0719904 0.0593221 0.848100
## 11: 6787.4584: 0.0574596 -0.0573165 0.0957600 0.0170137 0.0729269 0.0590613 0.851498
## 12: 6786.9905: 0.0574435 -0.0578171 0.0955500 0.0178711 0.0729353 0.0566919 0.855337
## 13: 6786.3007: 0.0574238 -0.0583268 0.0953934 0.0166574 0.0727417 0.0533564 0.858240
## 14: 6785.0358: 0.0573042 -0.0609257 0.0949264 0.0147055 0.0756105 0.0374833 0.873206
## 15: 6784.9513: 0.0573039 -0.0609300 0.0949275 0.0144428 0.0754729 0.0373121 0.873049
## 16: 6784.9178: 0.0573005 -0.0609769 0.0949412 0.0148881 0.0752191 0.0367046 0.872989
## 17: 6784.8955: 0.0572891 -0.0610873 0.0950334 0.0148109 0.0757447 0.0361657 0.872897
## 18: 6784.8194: 0.0572043 -0.0618735 0.0957554 0.0150197 0.0791459 0.0331976 0.872542
## 19: 6784.8080: 0.0569791 -0.0636508 0.0980053 0.0146289 0.0789961 0.0327952 0.872790
## 20: 6784.7182: 0.0567522 -0.0654953 0.100181 0.0148012 0.0789341 0.0327467 0.873255
## 21: 6784.2295: 0.0518477 -0.109835 0.139305 0.0136174 0.0757387 0.0313714 0.878754
## 22: 6784.1406: 0.0511277 -0.113360 0.147435 0.0135018 0.0758185 0.0301757 0.880208
## 23: 6784.0039: 0.0503543 -0.116973 0.149390 0.0138244 0.0803689 0.0257012 0.879560
## 24: 6784.0031: 0.0503540 -0.116965 0.149401 0.0137353 0.0804061 0.0256993 0.879575
## 25: 6784.0014: 0.0503509 -0.116926 0.149379 0.0137706 0.0804440 0.0256933 0.879620
## 26: 6784.0006: 0.0503467 -0.116889 0.149364 0.0137362 0.0804623 0.0256583 0.879637
## 27: 6783.9995: 0.0503375 -0.116818 0.149332 0.0137450 0.0805052 0.0256090 0.879689
## 28: 6783.9886: 0.0501455 -0.115640 0.148781 0.0136994 0.0808562 0.0245808 0.880245
## 29: 6783.9846: 0.0500002 -0.113680 0.146786 0.0136566 0.0810501 0.0244768 0.880418
## 30: 6783.9807: 0.0498245 -0.112089 0.145224 0.0135753 0.0811067 0.0244143 0.880404
## 31: 6783.9734: 0.0488638 -0.107401 0.141045 0.0136648 0.0811885 0.0248538 0.879887
## 32: 6783.9621: 0.0482468 -0.0977786 0.130713 0.0134019 0.0819212 0.0235134 0.880859
## 33: 6783.9523: 0.0474507 -0.105218 0.138210 0.0134022 0.0835961 0.0203012 0.882299
## 34: 6783.9500: 0.0474507 -0.105220 0.138209 0.0132982 0.0835712 0.0202772 0.882257
## 35: 6783.9484: 0.0474539 -0.105285 0.138273 0.0133313 0.0835901 0.0203023 0.882275
## 36: 6783.9481: 0.0474599 -0.105422 0.138394 0.0132626 0.0836327 0.0203670 0.882278
## 37: 6783.9477: 0.0474707 -0.105728 0.138694 0.0132844 0.0836298 0.0204006 0.882266
## 38: 6783.9464: 0.0475954 -0.110869 0.143667 0.0133533 0.0833928 0.0209793 0.881851
## 39: 6783.9463: 0.0474949 -0.108712 0.141564 0.0133731 0.0831606 0.0213533 0.881696
## 40: 6783.9463: 0.0477035 -0.113348 0.146237 0.0133731 0.0832319 0.0212893 0.881691
## 41: 6783.9463: 0.0475918 -0.111389 0.144202 0.0133688 0.0832613 0.0212018 0.881746
## 42: 6783.9463: 0.0475979 -0.111229 0.144069 0.0133695 0.0832390 0.0212428 0.881729
## 43: 6783.9463: 0.0476014 -0.111364 0.144201 0.0133697 0.0832420 0.0212388 0.881730
##
## Final Estimate of the Negative LLH:
## LLH: -14140.44 norm LLH: -2.538223
## mu ar1 ma1 omega alpha1
## 1.112838e-03 -1.113636e-01 1.442007e-01 7.307105e-06 8.324200e-02
## alpha2 beta1
## 2.123883e-02 8.817298e-01
##
## R-optimhess Difference Approximated Hessian Matrix:
## mu ar1 ma1 omega alpha1
## mu -1.549541e+07 -10973.6813 4394.0775 1.001200e+08 8.825238e+03
## ar1 -1.097368e+04 -5220.4525 -5213.6790 2.855247e+05 1.579227e+02
## ma1 4.394078e+03 -5213.6790 -5232.8327 2.416058e+05 1.471186e+02
## omega 1.001200e+08 285524.6926 241605.8057 -3.215057e+12 -5.470996e+08
## alpha1 8.825238e+03 157.9227 147.1186 -5.470996e+08 -1.621422e+05
## alpha2 9.952543e+02 199.6427 198.0982 -5.611563e+08 -1.616199e+05
## beta1 -1.252181e+04 -309.0611 -291.8503 -7.660070e+08 -1.853151e+05
## alpha2 beta1
## mu 9.952543e+02 -1.252181e+04
## ar1 1.996427e+02 -3.090611e+02
## ma1 1.980982e+02 -2.918503e+02
## omega -5.611563e+08 -7.660070e+08
## alpha1 -1.616199e+05 -1.853151e+05
## alpha2 -1.659141e+05 -1.908219e+05
## beta1 -1.908219e+05 -2.369930e+05
## attr(,"time")
## Time difference of 0.213238 secs
##
## --- END OF TRACE ---
##
##
## Time to Estimate Parameters:
## Time difference of 0.802696 secs
##
## Title:
## GARCH Modelling
##
## Call:
## garchFit(formula = ~arma(1, 1) + garch(2, 1), data = d.series.name,
## include.mean = TRUE)
##
## Mean and Variance Equation:
## data ~ arma(1, 1) + garch(2, 1)
## <environment: 0x7fd1bdddbaa0>
## [data = d.series.name]
##
## Conditional Distribution:
## norm
##
## Coefficient(s):
## mu ar1 ma1 omega alpha1
## 1.1128e-03 -1.1136e-01 1.4420e-01 7.3071e-06 8.3242e-02
## alpha2 beta1
## 2.1239e-02 8.8173e-01
##
## Std. Errors:
## based on Hessian
##
## Error Analysis:
## Estimate Std. Error t value Pr(>|t|)
## mu 1.113e-03 3.965e-04 2.807 0.005 **
## ar1 -1.114e-01 3.066e-01 -0.363 0.716
## ma1 1.442e-01 3.060e-01 0.471 0.637
## omega 7.307e-06 1.445e-06 5.056 4.29e-07 ***
## alpha1 8.324e-02 1.467e-02 5.673 1.41e-08 ***
## alpha2 2.124e-02 1.906e-02 1.114 0.265
## beta1 8.817e-01 1.257e-02 70.121 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Log Likelihood:
## 14140.44 normalized: 2.538223
##
## Description:
## Thu Jan 7 16:12:16 2016 by user:
##
##
## Standardised Residuals Tests:
## Statistic p-Value
## Jarque-Bera Test R Chi^2 383.587 0
## Shapiro-Wilk Test R W NA NA
## Ljung-Box Test R Q(10) 22.13172 0.01444747
## Ljung-Box Test R Q(15) 34.83257 0.002597619
## Ljung-Box Test R Q(20) 49.09035 0.0002985119
## Ljung-Box Test R^2 Q(10) 21.52159 0.0177362
## Ljung-Box Test R^2 Q(15) 24.39986 0.05860695
## Ljung-Box Test R^2 Q(20) 36.64023 0.01291958
## LM Arch Test R TR^2 23.01995 0.02755703
##
## Information Criterion Statistics:
## AIC BIC SIC HQIC
## -5.073933 -5.065608 -5.073936 -5.071031
# Itau
stock.name <- "ITSA4.SA"
stock.description <- "Itausa - Investimentos Itau S.A"
# Call your function and pass x and y to the function
run <- generateAnalysis(stock.name,stock.description)## time series starts 2000-01-03
## 'zoo' series from 2000-01-03 to 2016-01-06
## Data: num [1:3989, 1] 1.14 1.03 1.12 1.13 1.13 ...
## - attr(*, "dimnames")=List of 2
## ..$ : NULL
## ..$ : chr "AdjClose"
## Index: Date[1:3989], format: "2000-01-03" "2000-01-04" "2000-01-05" "2000-01-06" ...
## 'zoo' series from 2000-01-03 to 2015-09-30
## Data: num [1:3919] 1.14 1.03 1.12 1.13 1.13 ...
## Index: Date[1:3919], format: "2000-01-03" "2000-01-04" "2000-01-05" "2000-01-06" ...
## Warning in adf.test(d.series.name): p-value smaller than printed p-value
## Warning in sqrt(diag(fit$var.coef)): NaNs produced
##
## Title:
## ARIMA Modelling
##
## Call:
## armaFit(formula = ~arma(1, 3), data = d.series.name)
##
## Model:
## ARIMA(1,0,3) with method: CSS-ML
##
## Coefficient(s):
## ar1 ma1 ma2 ma3 intercept
## -0.4622035 0.4578396 -0.0348802 -0.0624000 0.0004784
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.1513910 -0.0126070 -0.0004014 0.0120342 0.2207431
##
## Moments:
## Skewness Kurtosis
## 0.1585 5.8397
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## ar1 -0.4622035 NA NA NA
## ma1 0.4578396 NA NA NA
## ma2 -0.0348802 0.0180969 -1.927 0.053928 .
## ma3 -0.0624000 0.0160788 -3.881 0.000104 ***
## intercept 0.0004784 0.0003490 1.371 0.170464
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## sigma^2 estimated as: 0.00055
## log likelihood: 9144.02
## AIC Criterion: -18276.04
##
## Description:
## Thu Jan 7 16:12:23 2016 by user:
##
## Series Initialization:
## ARMA Model: arma
## Formula Mean: ~ arma(1, 1)
## GARCH Model: garch
## Formula Variance: ~ garch(2, 1)
## ARMA Order: 1 1
## Max ARMA Order: 1
## GARCH Order: 2 1
## Max GARCH Order: 2
## Maximum Order: 2
## Conditional Dist: norm
## h.start: 3
## llh.start: 1
## Length of Series: 3918
## Recursion Init: mci
## Series Scale: 0.02349959## Warning in arima(.series$x, order = c(u, 0, v), include.mean =
## include.mean): possible convergence problem: optim gave code = 1
## Parameter Initialization:
## Initial Parameters: $params
## Limits of Transformations: $U, $V
## Which Parameters are Fixed? $includes
## Parameter Matrix:
## U V params includes
## mu -0.19735249 0.1973525 0.02116543 TRUE
## ar1 -0.99999999 1.0000000 -0.55064704 TRUE
## ma1 -0.99999999 1.0000000 0.54580383 TRUE
## omega 0.00000100 100.0000000 0.10000000 TRUE
## alpha1 0.00000001 1.0000000 0.05000000 TRUE
## alpha2 0.00000001 1.0000000 0.05000000 TRUE
## gamma1 -0.99999999 1.0000000 0.10000000 FALSE
## gamma2 -0.99999999 1.0000000 0.10000000 FALSE
## beta1 0.00000001 1.0000000 0.80000000 TRUE
## delta 0.00000000 2.0000000 2.00000000 FALSE
## skew 0.10000000 10.0000000 1.00000000 FALSE
## shape 1.00000000 10.0000000 4.00000000 FALSE
## Index List of Parameters to be Optimized:
## mu ar1 ma1 omega alpha1 alpha2 beta1
## 1 2 3 4 5 6 9
## Persistence: 0.9
##
##
## --- START OF TRACE ---
## Selected Algorithm: nlminb
##
## R coded nlminb Solver:
##
## 0: 5242.2289: 0.0211654 -0.550647 0.545804 0.100000 0.0500000 0.0500000 0.800000
## 1: 5237.9398: 0.0211656 -0.550584 0.545775 0.0939968 0.0490868 0.0485212 0.796818
## 2: 5234.0814: 0.0211666 -0.550259 0.545674 0.0863456 0.0586183 0.0554934 0.799969
## 3: 5232.4526: 0.0211668 -0.550164 0.545682 0.0827873 0.0576379 0.0541377 0.798412
## 4: 5231.1120: 0.0211684 -0.549485 0.545760 0.0768023 0.0632714 0.0571542 0.803834
## 5: 5228.4869: 0.0211732 -0.547391 0.546017 0.0634602 0.0616730 0.0493813 0.817273
## 6: 5224.4317: 0.0211792 -0.546533 0.544587 0.0575780 0.0627765 0.0425538 0.835734
## 7: 5215.2208: 0.0212023 -0.551108 0.531163 0.0259704 0.0622625 0.00725046 0.901836
## 8: 5214.9234: 0.0212023 -0.551028 0.531228 0.0265262 0.0625851 0.00748926 0.902286
## 9: 5214.8008: 0.0212028 -0.550154 0.531939 0.0265851 0.0622761 0.00620402 0.902614
## 10: 5214.5388: 0.0212107 -0.546809 0.532779 0.0270990 0.0624737 0.00640765 0.902971
## 11: 5214.4154: 0.0212189 -0.543425 0.533580 0.0268713 0.0621906 0.00616550 0.902723
## 12: 5214.4069: 0.0212276 -0.540025 0.534245 0.0273328 0.0623636 0.00639938 0.902906
## 13: 5214.3535: 0.0212336 -0.538571 0.533713 0.0272686 0.0625448 0.00584667 0.902361
## 14: 5214.3057: 0.0212329 -0.539762 0.532631 0.0274683 0.0631157 0.00542864 0.902354
## 15: 5214.2823: 0.0212456 -0.537773 0.530303 0.0272307 0.0640549 0.00411904 0.902070
## 16: 5214.1604: 0.0212585 -0.534537 0.529278 0.0276119 0.0646694 0.00389914 0.902135
## 17: 5214.1006: 0.0212858 -0.528582 0.526218 0.0264993 0.0649148 0.00298597 0.903237
## 18: 5214.0354: 0.0213236 -0.528870 0.513870 0.0244897 0.0613136 0.00410330 0.908325
## 19: 5214.0085: 0.0213237 -0.528819 0.513907 0.0246519 0.0614323 0.00412083 0.908466
## 20: 5213.9899: 0.0213238 -0.528713 0.513986 0.0246078 0.0614356 0.00390835 0.908465
## 21: 5213.9696: 0.0213255 -0.528374 0.513781 0.0247883 0.0616028 0.00377062 0.908581
## 22: 5213.9422: 0.0213298 -0.527716 0.513123 0.0247787 0.0616677 0.00346540 0.908431
## 23: 5213.9081: 0.0213387 -0.526378 0.511765 0.0250607 0.0620297 0.00317671 0.908370
## 24: 5213.8574: 0.0213573 -0.523642 0.508996 0.0251212 0.0624005 0.00278153 0.907931
## 25: 5213.6207: 0.0215468 -0.495338 0.484540 0.0244704 0.0635385 0.00417500 0.906968
## 26: 5213.4552: 0.0217446 -0.468101 0.459081 0.0254614 0.0623108 0.00246697 0.906866
## 27: 5213.4479: 0.0219552 -0.442049 0.432787 0.0276590 0.0645128 0.00152952 0.905667
## 28: 5213.1813: 0.0220374 -0.437776 0.427382 0.0277873 0.0661175 0.000118229 0.903692
## 29: 5213.1167: 0.0221486 -0.434467 0.426867 0.0264039 0.0625110 0.00208115 0.907099
## 30: 5213.0916: 0.0221487 -0.434445 0.426880 0.0260543 0.0626483 0.00197831 0.907099
## 31: 5213.0692: 0.0221534 -0.434381 0.426818 0.0261019 0.0628864 0.00203949 0.907252
## 32: 5213.0483: 0.0221653 -0.434100 0.426532 0.0258801 0.0630060 0.00189263 0.907192
## 33: 5213.0248: 0.0221881 -0.433403 0.425819 0.0259048 0.0633145 0.00185943 0.907282
## 34: 5212.9961: 0.0222300 -0.431813 0.424211 0.0257431 0.0635391 0.00162834 0.907165
## 35: 5212.9575: 0.0223075 -0.428398 0.420799 0.0258311 0.0639807 0.00144657 0.907152
## 36: 5212.8054: 0.0232118 -0.394487 0.387162 0.0261158 0.0654414 1.00000e-08 0.906061
## 37: 5212.5833: 0.0257159 -0.422872 0.412330 0.0248318 0.0674655 1.00000e-08 0.906331
## 38: 5212.5678: 0.0257159 -0.422846 0.412353 0.0249798 0.0675083 1.00000e-08 0.906457
## 39: 5212.5558: 0.0257163 -0.422627 0.412545 0.0249481 0.0670954 1.00000e-08 0.906549
## 40: 5212.5439: 0.0257363 -0.422570 0.412535 0.0250631 0.0671285 1.00000e-08 0.906673
## 41: 5212.5356: 0.0257766 -0.422421 0.412537 0.0249879 0.0669704 1.00000e-08 0.906720
## 42: 5212.5232: 0.0258577 -0.422252 0.412417 0.0250455 0.0669515 1.00000e-08 0.906842
## 43: 5211.5509: 0.0445587 -0.388189 0.377516 0.0224797 0.0597943 1.00000e-08 0.915669
## 44: 5211.2496: 0.0516639 -0.377569 0.375124 0.0244132 0.0634322 1.00000e-08 0.910325
## 45: 5211.1828: 0.0574399 -0.447700 0.442259 0.0234704 0.0650098 1.00000e-08 0.910459
## 46: 5211.1390: 0.0582842 -0.423568 0.415022 0.0235889 0.0658549 1.00000e-08 0.909636
## 47: 5211.1121: 0.0572153 -0.412415 0.405121 0.0238046 0.0654789 1.00000e-08 0.909554
## 48: 5211.1087: 0.0565741 -0.406631 0.399915 0.0238993 0.0652300 1.00000e-08 0.909608
## 49: 5211.1087: 0.0565897 -0.406560 0.399838 0.0239019 0.0652405 1.00000e-08 0.909592
## 50: 5211.1087: 0.0565884 -0.406549 0.399826 0.0239017 0.0652404 1.00000e-08 0.909593
##
## Final Estimate of the Negative LLH:
## LLH: -9484.418 norm LLH: -2.420729
## mu ar1 ma1 omega alpha1
## 1.329805e-03 -4.065493e-01 3.998263e-01 1.319924e-05 6.524036e-02
## alpha2 beta1
## 1.000000e-08 9.095929e-01
##
## R-optimhess Difference Approximated Hessian Matrix:
## mu ar1 ma1 omega
## mu -5024279.809 -3118.73091 1471.74511 -6.502179e+07
## ar1 -3118.731 -4103.35508 -4052.80869 -3.332937e+05
## ma1 1471.745 -4052.80869 -4075.27825 -2.683192e+05
## omega -65021785.290 -333293.72547 -268319.17123 -1.540547e+12
## alpha1 -2086.051 237.30353 248.60591 -4.750227e+08
## alpha2 -4629.759 23.75007 30.52669 -4.797590e+08
## beta1 -24801.877 -465.62881 -438.75675 -6.097617e+08
## alpha1 alpha2 beta1
## mu -2.086051e+03 -4.629759e+03 -2.480188e+04
## ar1 2.373035e+02 2.375007e+01 -4.656288e+02
## ma1 2.486059e+02 3.052669e+01 -4.387568e+02
## omega -4.750227e+08 -4.797590e+08 -6.097617e+08
## alpha1 -2.035722e+05 -2.024629e+05 -2.224960e+05
## alpha2 -2.024629e+05 -2.062615e+05 -2.265880e+05
## beta1 -2.224960e+05 -2.265880e+05 -2.702168e+05
## attr(,"time")
## Time difference of 0.1453691 secs
##
## --- END OF TRACE ---
##
##
## Time to Estimate Parameters:
## Time difference of 0.6953762 secs
##
## Title:
## GARCH Modelling
##
## Call:
## garchFit(formula = ~arma(1, 1) + garch(2, 1), data = d.series.name,
## include.mean = TRUE)
##
## Mean and Variance Equation:
## data ~ arma(1, 1) + garch(2, 1)
## <environment: 0x7fd1b9071f08>
## [data = d.series.name]
##
## Conditional Distribution:
## norm
##
## Coefficient(s):
## mu ar1 ma1 omega alpha1
## 1.3298e-03 -4.0655e-01 3.9983e-01 1.3199e-05 6.5240e-02
## alpha2 beta1
## 1.0000e-08 9.0959e-01
##
## Std. Errors:
## based on Hessian
##
## Error Analysis:
## Estimate Std. Error t value Pr(>|t|)
## mu 1.330e-03 4.606e-04 2.887 0.003885 **
## ar1 -4.065e-01 1.206e-01 -3.370 0.000752 ***
## ma1 3.998e-01 1.210e-01 3.303 0.000956 ***
## omega 1.320e-05 3.164e-06 4.171 3.03e-05 ***
## alpha1 6.524e-02 1.460e-02 4.468 7.88e-06 ***
## alpha2 1.000e-08 1.823e-02 0.000 1.000000
## beta1 9.096e-01 1.411e-02 64.487 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Log Likelihood:
## 9484.418 normalized: 2.420729
##
## Description:
## Thu Jan 7 16:12:25 2016 by user:
##
##
## Standardised Residuals Tests:
## Statistic p-Value
## Jarque-Bera Test R Chi^2 972.8185 0
## Shapiro-Wilk Test R W 0.9809267 0
## Ljung-Box Test R Q(10) 18.93227 0.04113149
## Ljung-Box Test R Q(15) 22.2451 0.1015363
## Ljung-Box Test R Q(20) 26.26359 0.1572818
## Ljung-Box Test R^2 Q(10) 8.41126 0.5887326
## Ljung-Box Test R^2 Q(15) 11.84018 0.6910838
## Ljung-Box Test R^2 Q(20) 13.71289 0.8447494
## LM Arch Test R TR^2 10.65483 0.5587085
##
## Information Criterion Statistics:
## AIC BIC SIC HQIC
## -4.837886 -4.826677 -4.837892 -4.833908
# BBAS3.SA
stock.name <- "BBAS3.SA"
stock.description <- "Banco do Brasil S.A."
# Call your function and pass x and y to the function
run <- generateAnalysis(stock.name,stock.description)## time series starts 2000-01-03
## 'zoo' series from 2000-01-03 to 2016-01-06
## Data: num [1:4134, 1] 1.86 1.78 1.79 1.82 1.78 ...
## - attr(*, "dimnames")=List of 2
## ..$ : NULL
## ..$ : chr "AdjClose"
## Index: Date[1:4134], format: "2000-01-03" "2000-01-04" "2000-01-05" "2000-01-06" ...
## 'zoo' series from 2000-01-03 to 2015-09-30
## Data: num [1:4064] 1.86 1.78 1.79 1.82 1.78 ...
## Index: Date[1:4064], format: "2000-01-03" "2000-01-04" "2000-01-05" "2000-01-06" ...
## Warning in adf.test(d.series.name): p-value smaller than printed p-value
## Warning in sqrt(diag(fit$var.coef)): NaNs produced
##
## Title:
## ARIMA Modelling
##
## Call:
## armaFit(formula = ~arma(1, 3), data = d.series.name)
##
## Model:
## ARIMA(1,0,3) with method: CSS-ML
##
## Coefficient(s):
## ar1 ma1 ma2 ma3 intercept
## -0.0060656 -0.0058871 -0.0409494 -0.0208757 0.0005117
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.164227 -0.015215 -0.000486 0.014395 0.256153
##
## Moments:
## Skewness Kurtosis
## 0.405 5.096
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## ar1 -0.0060656 NA NA NA
## ma1 -0.0058871 NA NA NA
## ma2 -0.0409494 0.0112843 -3.629 0.000285 ***
## ma3 -0.0208757 NA NA NA
## intercept 0.0005117 0.0003929 1.302 0.192872
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## sigma^2 estimated as: 0.0007293
## log likelihood: 8909.2
## AIC Criterion: -17806.4
##
## Description:
## Thu Jan 7 16:12:32 2016 by user:
##
## Series Initialization:
## ARMA Model: arma
## Formula Mean: ~ arma(1, 1)
## GARCH Model: garch
## Formula Variance: ~ garch(2, 1)
## ARMA Order: 1 1
## Max ARMA Order: 1
## GARCH Order: 2 1
## Max GARCH Order: 2
## Maximum Order: 2
## Conditional Dist: norm
## h.start: 3
## llh.start: 1
## Length of Series: 4063
## Recursion Init: mci
## Series Scale: 0.02703795
##
## Parameter Initialization:
## Initial Parameters: $params
## Limits of Transformations: $U, $V
## Which Parameters are Fixed? $includes
## Parameter Matrix:
## U V params includes
## mu -0.18874661 0.1887466 0.01904071 TRUE
## ar1 -0.99999999 1.0000000 0.80929497 TRUE
## ma1 -0.99999999 1.0000000 -0.83740229 TRUE
## omega 0.00000100 100.0000000 0.10000000 TRUE
## alpha1 0.00000001 1.0000000 0.05000000 TRUE
## alpha2 0.00000001 1.0000000 0.05000000 TRUE
## gamma1 -0.99999999 1.0000000 0.10000000 FALSE
## gamma2 -0.99999999 1.0000000 0.10000000 FALSE
## beta1 0.00000001 1.0000000 0.80000000 TRUE
## delta 0.00000000 2.0000000 2.00000000 FALSE
## skew 0.10000000 10.0000000 1.00000000 FALSE
## shape 1.00000000 10.0000000 4.00000000 FALSE
## Index List of Parameters to be Optimized:
## mu ar1 ma1 omega alpha1 alpha2 beta1
## 1 2 3 4 5 6 9
## Persistence: 0.9
##
##
## --- START OF TRACE ---
## Selected Algorithm: nlminb
##
## R coded nlminb Solver:
##
## 0: 5457.7021: 0.0190407 0.809295 -0.837402 0.100000 0.0500000 0.0500000 0.800000
## 1: 5448.6455: 0.0190333 0.809199 -0.834878 0.0898797 0.0507276 0.0487420 0.794443
## 2: 5442.4595: 0.0190236 0.808766 -0.831926 0.0880050 0.0597887 0.0549643 0.797348
## 3: 5436.5735: 0.0189974 0.806754 -0.824995 0.0676468 0.0673191 0.0555951 0.790851
## 4: 5426.8513: 0.0189407 0.798334 -0.814997 0.0652965 0.0841722 0.0589047 0.800200
## 5: 5420.4644: 0.0188657 0.784193 -0.805863 0.0579554 0.0894687 0.0462582 0.805367
## 6: 5416.9488: 0.0187997 0.778746 -0.791786 0.0567519 0.0924213 0.0337040 0.818015
## 7: 5411.1657: 0.0186981 0.754159 -0.790889 0.0405494 0.0982159 0.0129089 0.848153
## 8: 5409.6293: 0.0186719 0.759843 -0.777127 0.0404720 0.101467 0.00912333 0.853256
## 9: 5409.5664: 0.0186700 0.759460 -0.776985 0.0374766 0.0999155 0.00701396 0.851326
## 10: 5408.4942: 0.0186691 0.759285 -0.776914 0.0388619 0.100879 0.00773575 0.852562
## 11: 5407.4262: 0.0186218 0.751330 -0.772654 0.0326713 0.103274 1.00000e-08 0.861096
## 12: 5406.9004: 0.0185367 0.750639 -0.759479 0.0221562 0.0955143 1.00000e-08 0.887414
## 13: 5405.3621: 0.0183701 0.730910 -0.742211 0.0287930 0.0798802 1.00000e-08 0.889404
## 14: 5404.8361: 0.0183677 0.729857 -0.742672 0.0262364 0.0815154 1.00000e-08 0.889227
## 15: 5404.3376: 0.0183585 0.728159 -0.743030 0.0275763 0.0838154 1.00000e-08 0.888734
## 16: 5403.9274: 0.0183443 0.726283 -0.742894 0.0272582 0.0849910 1.00000e-08 0.886500
## 17: 5403.5756: 0.0183045 0.722359 -0.741023 0.0283237 0.0882731 1.00000e-08 0.883843
## 18: 5403.0839: 0.0182023 0.716253 -0.732228 0.0286535 0.0908636 1.00000e-08 0.879550
## 19: 5402.2631: 0.0179607 0.699365 -0.723518 0.0244125 0.0840242 1.00000e-08 0.891236
## 20: 5402.2469: 0.0179604 0.699353 -0.723432 0.0245137 0.0842343 1.00000e-08 0.891350
## 21: 5402.2338: 0.0179598 0.699333 -0.723308 0.0243106 0.0843181 1.00000e-08 0.891248
## 22: 5402.2118: 0.0179556 0.699125 -0.722936 0.0243911 0.0845517 1.00000e-08 0.891348
## 23: 5401.0713: 0.0173478 0.667337 -0.681638 0.0245180 0.0839128 1.00000e-08 0.891089
## 24: 5401.0639: 0.0168868 0.635310 -0.661188 0.0386075 0.103786 1.00000e-08 0.857628
## 25: 5401.0000: 0.0168865 0.635342 -0.661084 0.0377197 0.103691 1.00000e-08 0.857496
## 26: 5400.9324: 0.0168928 0.635295 -0.660886 0.0377216 0.104160 1.00000e-08 0.858170
## 27: 5400.8528: 0.0169168 0.635010 -0.660382 0.0366528 0.104158 1.00000e-08 0.858633
## 28: 5400.7481: 0.0169731 0.634169 -0.659375 0.0362502 0.104002 1.00000e-08 0.860192
## 29: 5400.1747: 0.0179237 0.617377 -0.642442 0.0295881 0.0896161 1.00000e-08 0.880114
## 30: 5400.0218: 0.0179224 0.617490 -0.642002 0.0277450 0.0913318 1.00000e-08 0.880619
## 31: 5399.9862: 0.0179588 0.616322 -0.640785 0.0279554 0.0914910 1.00000e-08 0.881031
## 32: 5399.6615: 0.0191170 0.575338 -0.599814 0.0262848 0.0898151 1.00000e-08 0.884505
## 33: 5399.3155: 0.0191219 0.501956 -0.523692 0.0296181 0.0948942 1.00000e-08 0.875759
## 34: 5399.1778: 0.0223768 0.444831 -0.465234 0.0284471 0.0932548 1.00000e-08 0.878672
## 35: 5399.1115: 0.0232857 0.380784 -0.396861 0.0244319 0.0872102 1.00000e-08 0.889054
## 36: 5399.0129: 0.0268406 0.316476 -0.331474 0.0261076 0.0898021 1.00000e-08 0.884730
## 37: 5398.9539: 0.0308399 0.223219 -0.234907 0.0266919 0.0908727 1.00000e-08 0.883051
## 38: 5398.8284: 0.0423643 -0.0574740 0.0561819 0.0270880 0.0917394 1.00000e-08 0.881813
## 39: 5398.8228: 0.0438001 -0.0955279 0.0952419 0.0268938 0.0914146 1.00000e-08 0.882334
## 40: 5398.8150: 0.0430796 -0.0902748 0.0886937 0.0262144 0.0901917 1.00000e-08 0.884228
## 41: 5398.8139: 0.0429202 -0.0916798 0.0902033 0.0262305 0.0902800 1.00000e-08 0.884140
## 42: 5398.8123: 0.0421547 -0.0913749 0.0900517 0.0263205 0.0904446 1.00000e-08 0.883888
## 43: 5398.8123: 0.0421367 -0.0915237 0.0901895 0.0263244 0.0904327 1.00000e-08 0.883891
## 44: 5398.8123: 0.0421368 -0.0915425 0.0902024 0.0263260 0.0904336 1.00000e-08 0.883888
##
## Final Estimate of the Negative LLH:
## LLH: -9270.706 norm LLH: -2.281739
## mu ar1 ma1 omega alpha1
## 1.139292e-03 -9.154249e-02 9.020237e-02 1.924567e-05 9.043359e-02
## alpha2 beta1
## 1.000000e-08 8.838878e-01
##
## R-optimhess Difference Approximated Hessian Matrix:
## mu ar1 ma1 omega
## mu -6676604.439 -5272.29968 1637.1636 -6.540905e+07
## ar1 -5272.300 -3621.26368 -3538.6041 -6.970961e+05
## ma1 1637.164 -3538.60409 -3470.5155 -6.281187e+05
## omega -65409048.823 -697096.10169 -628118.6838 -6.133251e+11
## alpha1 -3141.074 139.63518 143.5760 -2.265238e+08
## alpha2 -3999.005 177.92623 182.5247 -2.271179e+08
## beta1 -19422.674 -7.74186 13.3349 -3.055991e+08
## alpha1 alpha2 beta1
## mu -3.141074e+03 -3.999005e+03 -1.942267e+04
## ar1 1.396352e+02 1.779262e+02 -7.741860e+00
## ma1 1.435760e+02 1.825247e+02 1.333490e+01
## omega -2.265238e+08 -2.271179e+08 -3.055991e+08
## alpha1 -1.236337e+05 -1.219342e+05 -1.385106e+05
## alpha2 -1.219342e+05 -1.236885e+05 -1.397871e+05
## beta1 -1.385106e+05 -1.397871e+05 -1.715156e+05
## attr(,"time")
## Time difference of 0.1562271 secs
##
## --- END OF TRACE ---
##
##
## Time to Estimate Parameters:
## Time difference of 0.733258 secs
##
## Title:
## GARCH Modelling
##
## Call:
## garchFit(formula = ~arma(1, 1) + garch(2, 1), data = d.series.name,
## include.mean = TRUE)
##
## Mean and Variance Equation:
## data ~ arma(1, 1) + garch(2, 1)
## <environment: 0x7fd1bbc0f5b8>
## [data = d.series.name]
##
## Conditional Distribution:
## norm
##
## Coefficient(s):
## mu ar1 ma1 omega alpha1
## 1.1393e-03 -9.1542e-02 9.0202e-02 1.9246e-05 9.0434e-02
## alpha2 beta1
## 1.0000e-08 8.8389e-01
##
## Std. Errors:
## based on Hessian
##
## Error Analysis:
## Estimate Std. Error t value Pr(>|t|)
## mu 1.139e-03 5.747e-04 1.982 0.0474 *
## ar1 -9.154e-02 4.078e-01 -0.224 0.8224
## ma1 9.020e-02 4.163e-01 0.217 0.8285
## omega 1.925e-05 7.174e-06 2.683 0.0073 **
## alpha1 9.043e-02 1.717e-02 5.266 1.39e-07 ***
## alpha2 1.000e-08 2.491e-02 0.000 1.0000
## beta1 8.839e-01 2.731e-02 32.360 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Log Likelihood:
## 9270.706 normalized: 2.281739
##
## Description:
## Thu Jan 7 16:12:34 2016 by user:
##
##
## Standardised Residuals Tests:
## Statistic p-Value
## Jarque-Bera Test R Chi^2 453.9605 0
## Shapiro-Wilk Test R W 0.9879195 0
## Ljung-Box Test R Q(10) 6.359994 0.7841659
## Ljung-Box Test R Q(15) 9.014066 0.8767808
## Ljung-Box Test R Q(20) 11.17128 0.9416592
## Ljung-Box Test R^2 Q(10) 22.02592 0.01497309
## Ljung-Box Test R^2 Q(15) 27.53434 0.02467251
## Ljung-Box Test R^2 Q(20) 33.57461 0.02915051
## LM Arch Test R TR^2 21.8295 0.03947568
##
## Information Criterion Statistics:
## AIC BIC SIC HQIC
## -4.560032 -4.549162 -4.560038 -4.556182
# KROT3.SA
stock.name <- "KROT3.SA"
stock.description <- "Kroton Educacional S.A."
# Call your function and pass x and y to the function
run <- generateAnalysis(stock.name,stock.description)## time series starts 2012-03-14
## 'zoo' series from 2012-03-14 to 2016-01-06
## Data: num [1:994, 1] 2.21 2.21 2.21 2.21 2.21 ...
## - attr(*, "dimnames")=List of 2
## ..$ : NULL
## ..$ : chr "AdjClose"
## Index: Date[1:994], format: "2012-03-14" "2012-03-15" "2012-03-16" "2012-03-19" ...
## 'zoo' series from 2012-03-14 to 2015-09-30
## Data: num [1:924] 2.21 2.21 2.21 2.21 2.21 ...
## Index: Date[1:924], format: "2012-03-14" "2012-03-15" "2012-03-16" "2012-03-19" ...
## Warning in adf.test(d.series.name): p-value smaller than printed p-value
## Warning in lsfit(log10(M), log10(RS), wt): 29 missing values deleted
##
## Title:
## ARIMA Modelling
##
## Call:
## armaFit(formula = ~arma(1, 3), data = d.series.name)
##
## Model:
## ARIMA(1,0,3) with method: CSS-ML
##
## Coefficient(s):
## ar1 ma1 ma2 ma3 intercept
## 0.426797 -0.560552 0.053052 -0.238926 0.001384
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.391973 -0.011893 -0.001244 0.015092 1.275535
##
## Moments:
## Skewness Kurtosis
## -1.295 120.049
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## ar1 0.426797 0.076118 5.607 2.06e-08 ***
## ma1 -0.560552 0.074747 -7.499 6.42e-14 ***
## ma2 0.053052 0.043406 1.222 0.222
## ma3 -0.238926 0.031674 -7.543 4.57e-14 ***
## intercept 0.001384 0.001440 0.961 0.336
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## sigma^2 estimated as: 0.00969
## log likelihood: 829.97
## AIC Criterion: -1647.94
##
## Description:
## Thu Jan 7 16:12:36 2016 by user:
## Warning in lsfit(log10(M), log10(RS), wt): 29 missing values deleted
##
## Series Initialization:
## ARMA Model: arma
## Formula Mean: ~ arma(1, 1)
## GARCH Model: garch
## Formula Variance: ~ garch(2, 1)
## ARMA Order: 1 1
## Max ARMA Order: 1
## GARCH Order: 2 1
## Max GARCH Order: 2
## Maximum Order: 2
## Conditional Dist: norm
## h.start: 3
## llh.start: 1
## Length of Series: 923
## Recursion Init: mci
## Series Scale: 0.1033657
##
## Parameter Initialization:
## Initial Parameters: $params
## Limits of Transformations: $U, $V
## Which Parameters are Fixed? $includes
## Parameter Matrix:
## U V params includes
## mu -0.13042069 0.1304207 0.01305813 TRUE
## ar1 -0.99999999 1.0000000 -0.52596396 TRUE
## ma1 -0.99999999 1.0000000 0.45626181 TRUE
## omega 0.00000100 100.0000000 0.10000000 TRUE
## alpha1 0.00000001 1.0000000 0.05000000 TRUE
## alpha2 0.00000001 1.0000000 0.05000000 TRUE
## gamma1 -0.99999999 1.0000000 0.10000000 FALSE
## gamma2 -0.99999999 1.0000000 0.10000000 FALSE
## beta1 0.00000001 1.0000000 0.80000000 TRUE
## delta 0.00000000 2.0000000 2.00000000 FALSE
## skew 0.10000000 10.0000000 1.00000000 FALSE
## shape 1.00000000 10.0000000 4.00000000 FALSE
## Index List of Parameters to be Optimized:
## mu ar1 ma1 omega alpha1 alpha2 beta1
## 1 2 3 4 5 6 9
## Persistence: 0.9
##
##
## --- START OF TRACE ---
## Selected Algorithm: nlminb
##
## R coded nlminb Solver:
##
## 0: 967.58942: 0.0130581 -0.525964 0.456262 0.100000 0.0500000 0.0500000 0.800000
## 1: 946.80898: 0.0130581 -0.526246 0.455994 0.0849877 0.0504835 0.0491423 0.790264
## 2: 941.35280: 0.0130579 -0.526773 0.455496 0.0699198 0.0525607 0.0485962 0.780825
## 3: 938.20876: 0.0130572 -0.528770 0.453608 0.0805589 0.0637244 0.0496474 0.772176
## 4: 936.01889: 0.0130559 -0.531357 0.451178 0.0787447 0.0735573 0.0495962 0.757730
## 5: 933.89311: 0.0130500 -0.539192 0.443934 0.0959114 0.0833502 0.0517521 0.729877
## 6: 932.39394: 0.0130443 -0.545643 0.438012 0.0908191 0.107386 0.0757073 0.724335
## 7: 932.25930: 0.0130123 -0.553081 0.431147 0.0989278 0.0933489 0.0750350 0.694113
## 8: 931.78839: 0.0130120 -0.553271 0.430965 0.103134 0.0953226 0.0765080 0.696866
## 9: 931.60029: 0.0130114 -0.553655 0.430599 0.0991742 0.0985884 0.0786114 0.697459
## 10: 931.41811: 0.0129993 -0.556044 0.428190 0.101352 0.104982 0.0720578 0.702428
## 11: 931.25579: 0.0129763 -0.557703 0.426417 0.0985900 0.112384 0.0646962 0.702315
## 12: 931.17804: 0.0128827 -0.548232 0.435006 0.103903 0.124977 0.0654636 0.692311
## 13: 931.01319: 0.0126245 -0.573829 0.409419 0.0999748 0.136144 0.0549268 0.699869
## 14: 931.00259: 0.0126239 -0.573381 0.409825 0.0993139 0.136706 0.0553676 0.699628
## 15: 930.99164: 0.0126203 -0.572839 0.410271 0.0999484 0.137192 0.0554033 0.700031
## 16: 930.97702: 0.0126075 -0.571589 0.411215 0.0991066 0.138019 0.0547034 0.700456
## 17: 930.96119: 0.0125712 -0.569293 0.412759 0.0993224 0.139346 0.0531641 0.702003
## 18: 930.93498: 0.0124562 -0.567325 0.413003 0.0989396 0.138627 0.0551729 0.700851
## 19: 930.90891: 0.0122255 -0.566167 0.411178 0.100877 0.137685 0.0590722 0.697159
## 20: 930.87405: 0.0120102 -0.562354 0.412211 0.0997537 0.142229 0.0528290 0.698606
## 21: 930.85152: 0.0117723 -0.559090 0.414083 0.100088 0.143340 0.0528754 0.700270
## 22: 930.83165: 0.0115337 -0.557912 0.414836 0.0990335 0.141898 0.0561553 0.699591
## 23: 930.75889: 0.00971934 -0.551668 0.409794 0.0988277 0.151849 0.0433092 0.699115
## 24: 930.27939: -0.00114068 -0.516561 0.379595 0.103142 0.163531 0.0522702 0.688221
## 25: 930.01328: -0.0119426 -0.435956 0.322737 0.100179 0.166044 0.0446284 0.698160
## 26: 929.73136: -0.0226798 -0.354896 0.216785 0.101193 0.156178 0.0578991 0.694307
## 27: 929.60081: -0.0299643 -0.410601 0.275530 0.102152 0.132696 0.0777366 0.690777
## 28: 929.55580: -0.0329053 -0.477743 0.335559 0.101214 0.132565 0.0781253 0.692050
## 29: 929.55554: -0.0348876 -0.436081 0.284208 0.100764 0.130674 0.0805701 0.692226
## 30: 929.55057: -0.0341590 -0.465515 0.317678 0.100888 0.131164 0.0797313 0.692133
## 31: 929.55056: -0.0341556 -0.464813 0.317285 0.100891 0.131355 0.0795513 0.692152
## 32: 929.55055: -0.0341711 -0.465080 0.317505 0.100891 0.131290 0.0795890 0.692155
## 33: 929.55055: -0.0341724 -0.465094 0.317513 0.100890 0.131296 0.0795832 0.692155
##
## Final Estimate of the Negative LLH:
## LLH: -1165.182 norm LLH: -1.262385
## mu ar1 ma1 omega alpha1
## -0.003532254 -0.465093595 0.317512574 0.001077959 0.131295992
## alpha2 beta1
## 0.079583204 0.692155043
##
## R-optimhess Difference Approximated Hessian Matrix:
## mu ar1 ma1 omega alpha1
## mu -128480.59912 197.32587 -99.984334 6.906563e+05 -575.83877
## ar1 197.32587 -217.76756 -201.662115 6.182968e+03 55.48211
## ma1 -99.98433 -201.66211 -194.416743 1.006964e+04 42.66468
## omega 690656.27134 6182.96839 10069.639030 -3.158162e+08 -97893.80662
## alpha1 -575.83877 55.48211 42.664676 -9.789381e+04 -1099.55414
## alpha2 -2774.72114 14.70127 -7.695865 -8.393257e+04 -1090.21732
## beta1 -228.62597 88.37801 88.268715 -1.154244e+06 -1584.54527
## alpha2 beta1
## mu -2774.721135 -2.286260e+02
## ar1 14.701266 8.837801e+01
## ma1 -7.695865 8.826871e+01
## omega -83932.570964 -1.154244e+06
## alpha1 -1090.217315 -1.584545e+03
## alpha2 -1560.334134 -2.090775e+03
## beta1 -2090.775041 -7.710301e+03
## attr(,"time")
## Time difference of 0.05019403 secs
##
## --- END OF TRACE ---
##
##
## Time to Estimate Parameters:
## Time difference of 0.14305 secs
##
## Title:
## GARCH Modelling
##
## Call:
## garchFit(formula = ~arma(1, 1) + garch(2, 1), data = d.series.name,
## include.mean = TRUE)
##
## Mean and Variance Equation:
## data ~ arma(1, 1) + garch(2, 1)
## <environment: 0x7fd1b57e64e0>
## [data = d.series.name]
##
## Conditional Distribution:
## norm
##
## Coefficient(s):
## mu ar1 ma1 omega alpha1 alpha2
## -0.0035323 -0.4650936 0.3175126 0.0010780 0.1312960 0.0795832
## beta1
## 0.6921550
##
## Std. Errors:
## based on Hessian
##
## Error Analysis:
## Estimate Std. Error t value Pr(>|t|)
## mu -0.0035323 0.0030173 -1.171 0.2417
## ar1 -0.4650936 0.3648070 -1.275 0.2023
## ma1 0.3175126 0.3879403 0.818 0.4131
## omega 0.0010780 0.0001064 10.134 <2e-16 ***
## alpha1 0.1312960 0.0569969 2.304 0.0212 *
## alpha2 0.0795832 0.0594417 1.339 0.1806
## beta1 0.6921550 0.0270258 25.611 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Log Likelihood:
## 1165.182 normalized: 1.262385
##
## Description:
## Thu Jan 7 16:12:37 2016 by user:
##
##
## Standardised Residuals Tests:
## Statistic p-Value
## Jarque-Bera Test R Chi^2 3935116 0
## Shapiro-Wilk Test R W 0.3097579 0
## Ljung-Box Test R Q(10) 27.76416 0.001968995
## Ljung-Box Test R Q(15) 39.54696 0.0005306483
## Ljung-Box Test R Q(20) 40.11346 0.004832976
## Ljung-Box Test R^2 Q(10) 5.702808 0.8395835
## Ljung-Box Test R^2 Q(15) 6.09349 0.9781342
## Ljung-Box Test R^2 Q(20) 6.132036 0.9987071
## LM Arch Test R TR^2 5.873323 0.9223325
##
## Information Criterion Statistics:
## AIC BIC SIC HQIC
## -2.509603 -2.472990 -2.509717 -2.495634
# VALE5.SA
stock.name <- "VALE5.SA"
stock.description <- "Vale S.A."
# Call your function and pass x and y to the function
run <- generateAnalysis(stock.name,stock.description)## time series starts 2003-01-01
## 'zoo' series from 2003-01-01 to 2016-01-06
## Data: num [1:3228, 1] 6.07 6.07 6 5.84 5.71 ...
## - attr(*, "dimnames")=List of 2
## ..$ : NULL
## ..$ : chr "AdjClose"
## Index: Date[1:3228], format: "2003-01-01" "2003-01-02" "2003-01-03" "2003-01-06" ...
## 'zoo' series from 2003-01-01 to 2015-09-30
## Data: num [1:3158] 6.07 6.07 6 5.84 5.71 ...
## Index: Date[1:3158], format: "2003-01-01" "2003-01-02" "2003-01-03" "2003-01-06" ...
## Warning in adf.test(d.series.name): p-value smaller than printed p-value
##
## Title:
## ARIMA Modelling
##
## Call:
## armaFit(formula = ~arma(1, 3), data = d.series.name)
##
## Model:
## ARIMA(1,0,3) with method: CSS-ML
##
## Coefficient(s):
## ar1 ma1 ma2 ma3 intercept
## -0.1147017 0.1352835 -0.0466870 -0.0628895 0.0002432
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.1591899 -0.0125681 0.0002449 0.0123261 0.1234791
##
## Moments:
## Skewness Kurtosis
## -0.0741 3.2827
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## ar1 -0.1147017 0.2806508 -0.409 0.68276
## ma1 0.1352835 0.2799768 0.483 0.62896
## ma2 -0.0466870 0.0185914 -2.511 0.01203 *
## ma3 -0.0628895 0.0207959 -3.024 0.00249 **
## intercept 0.0002432 0.0003799 0.640 0.52203
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## sigma^2 estimated as: 0.0005368
## log likelihood: 7406.32
## AIC Criterion: -14800.64
##
## Description:
## Thu Jan 7 16:12:40 2016 by user:
##
## Series Initialization:
## ARMA Model: arma
## Formula Mean: ~ arma(1, 1)
## GARCH Model: garch
## Formula Variance: ~ garch(2, 1)
## ARMA Order: 1 1
## Max ARMA Order: 1
## GARCH Order: 2 1
## Max GARCH Order: 2
## Maximum Order: 2
## Conditional Dist: norm
## h.start: 3
## llh.start: 1
## Length of Series: 3157
## Recursion Init: mci
## Series Scale: 0.02324454
##
## Parameter Initialization:
## Initial Parameters: $params
## Limits of Transformations: $U, $V
## Which Parameters are Fixed? $includes
## Parameter Matrix:
## U V params includes
## mu -0.10373679 0.1037368 0.01037722 TRUE
## ar1 -0.99999999 1.0000000 -0.29796748 TRUE
## ma1 -0.99999999 1.0000000 0.32712119 TRUE
## omega 0.00000100 100.0000000 0.10000000 TRUE
## alpha1 0.00000001 1.0000000 0.05000000 TRUE
## alpha2 0.00000001 1.0000000 0.05000000 TRUE
## gamma1 -0.99999999 1.0000000 0.10000000 FALSE
## gamma2 -0.99999999 1.0000000 0.10000000 FALSE
## beta1 0.00000001 1.0000000 0.80000000 TRUE
## delta 0.00000000 2.0000000 2.00000000 FALSE
## skew 0.10000000 10.0000000 1.00000000 FALSE
## shape 1.00000000 10.0000000 4.00000000 FALSE
## Index List of Parameters to be Optimized:
## mu ar1 ma1 omega alpha1 alpha2 beta1
## 1 2 3 4 5 6 9
## Persistence: 0.9
##
##
## --- START OF TRACE ---
## Selected Algorithm: nlminb
##
## R coded nlminb Solver:
##
## 0: 4220.5083: 0.0103772 -0.297967 0.327121 0.100000 0.0500000 0.0500000 0.800000
## 1: 4216.4468: 0.0103774 -0.296902 0.328160 0.0816230 0.0481218 0.0498433 0.791563
## 2: 4202.4737: 0.0103776 -0.295404 0.329616 0.0777685 0.0600405 0.0645020 0.797769
## 3: 4198.9154: 0.0103780 -0.292750 0.332172 0.0587052 0.0616100 0.0704353 0.797734
## 4: 4194.2747: 0.0103790 -0.287891 0.336765 0.0546845 0.0600077 0.0768558 0.815341
## 5: 4190.1470: 0.0103804 -0.284722 0.339464 0.0456379 0.0492084 0.0747525 0.829284
## 6: 4182.8614: 0.0103854 -0.293368 0.328157 0.0237297 0.0227754 0.0634317 0.889690
## 7: 4182.8353: 0.0103855 -0.293172 0.328344 0.0242027 0.0229698 0.0634197 0.890115
## 8: 4182.7486: 0.0103855 -0.292912 0.328582 0.0238916 0.0227839 0.0629200 0.890215
## 9: 4182.6518: 0.0103857 -0.292277 0.329168 0.0241073 0.0229477 0.0622721 0.891122
## 10: 4182.4173: 0.0103860 -0.291210 0.330102 0.0232492 0.0231238 0.0604766 0.892623
## 11: 4181.8799: 0.0103880 -0.288251 0.332266 0.0205962 0.0275671 0.0531453 0.899710
## 12: 4181.7725: 0.0103902 -0.287643 0.331915 0.0206318 0.0271576 0.0478972 0.902241
## 13: 4181.6885: 0.0103916 -0.287509 0.331421 0.0214289 0.0281363 0.0463689 0.904001
## 14: 4181.5292: 0.0103931 -0.288049 0.330189 0.0206087 0.0297673 0.0449076 0.903903
## 15: 4181.5001: 0.0103932 -0.287721 0.330471 0.0201571 0.0303208 0.0450884 0.904273
## 16: 4181.4903: 0.0103942 -0.287342 0.330390 0.0197856 0.0303187 0.0443849 0.904545
## 17: 4181.4478: 0.0103953 -0.287039 0.330247 0.0198494 0.0306317 0.0438646 0.905156
## 18: 4181.3822: 0.0104005 -0.285592 0.329373 0.0192441 0.0316866 0.0409189 0.907264
## 19: 4181.3710: 0.0104263 -0.279882 0.323830 0.0193311 0.0323208 0.0402627 0.908013
## 20: 4181.3098: 0.0104526 -0.273730 0.318727 0.0190792 0.0318363 0.0407459 0.907759
## 21: 4181.2973: 0.0104687 -0.271159 0.314781 0.0187759 0.0339347 0.0392624 0.907976
## 22: 4181.2557: 0.0105059 -0.262338 0.309281 0.0185062 0.0324165 0.0406556 0.907948
## 23: 4181.1332: 0.0107154 -0.225419 0.269950 0.0185378 0.0351948 0.0352990 0.909883
## 24: 4181.1144: 0.0107154 -0.225398 0.269969 0.0186356 0.0353079 0.0354033 0.909986
## 25: 4181.1067: 0.0107155 -0.225321 0.270037 0.0184745 0.0353859 0.0354492 0.909975
## 26: 4181.1030: 0.0107170 -0.225004 0.269834 0.0184924 0.0354696 0.0355134 0.910044
## 27: 4181.0977: 0.0107201 -0.224394 0.269340 0.0184091 0.0354496 0.0354811 0.910031
## 28: 4181.0908: 0.0107263 -0.223166 0.268353 0.0183983 0.0355081 0.0355120 0.910119
## 29: 4180.9833: 0.0109980 -0.172220 0.223144 0.0180002 0.0344977 0.0344766 0.912143
## 30: 4180.9145: 0.0114051 -0.128679 0.179729 0.0186784 0.0347649 0.0367378 0.909781
## 31: 4180.8614: 0.0120147 -0.0981896 0.148996 0.0186760 0.0350652 0.0374611 0.907772
## 32: 4180.6286: 0.0167261 -0.146222 0.195989 0.0160406 0.0423852 0.0262607 0.914594
## 33: 4179.9863: 0.0278852 -0.108362 0.160499 0.0179731 0.0452981 0.0268463 0.909684
## 34: 4179.8759: 0.0389712 -0.201948 0.254826 0.0190505 0.0349392 0.0366266 0.908425
## 35: 4179.7971: 0.0401254 -0.153606 0.203991 0.0186412 0.0361799 0.0364379 0.908242
## 36: 4179.7723: 0.0387613 -0.153286 0.204185 0.0186518 0.0387350 0.0342847 0.907902
## 37: 4179.7712: 0.0380231 -0.145066 0.196369 0.0185615 0.0395751 0.0330278 0.908373
## 38: 4179.7707: 0.0379510 -0.149362 0.200467 0.0185766 0.0395148 0.0333839 0.908112
## 39: 4179.7706: 0.0380834 -0.148776 0.199910 0.0185871 0.0394370 0.0334200 0.908129
## 40: 4179.7706: 0.0380611 -0.148700 0.199835 0.0185843 0.0394510 0.0334001 0.908138
## 41: 4179.7706: 0.0380622 -0.148710 0.199845 0.0185846 0.0394502 0.0334020 0.908137
##
## Final Estimate of the Negative LLH:
## LLH: -7695.869 norm LLH: -2.437716
## mu ar1 ma1 omega alpha1
## 8.847391e-04 -1.487097e-01 1.998448e-01 1.004141e-05 3.945024e-02
## alpha2 beta1
## 3.340199e-02 9.081366e-01
##
## R-optimhess Difference Approximated Hessian Matrix:
## mu ar1 ma1 omega
## mu -5804399.013 -3.054037e+03 1.286124e+03 -5.248985e+07
## ar1 -3054.037 -3.052770e+03 -3.071717e+03 -1.265958e+06
## ma1 1286.124 -3.071717e+03 -3.117684e+03 -1.186777e+06
## omega -52489849.142 -1.265958e+06 -1.186777e+06 -1.454973e+12
## alpha1 1319.787 6.021266e+01 5.899689e+01 -3.943726e+08
## alpha2 -7751.153 -3.789274e+01 -3.491994e+01 -3.932371e+08
## beta1 -28331.208 -5.595683e+02 -5.343574e+02 -5.055202e+08
## alpha1 alpha2 beta1
## mu 1.319787e+03 -7.751153e+03 -2.833121e+04
## ar1 6.021266e+01 -3.789274e+01 -5.595683e+02
## ma1 5.899689e+01 -3.491994e+01 -5.343574e+02
## omega -3.943726e+08 -3.932371e+08 -5.055202e+08
## alpha1 -1.605027e+05 -1.591281e+05 -1.736106e+05
## alpha2 -1.591281e+05 -1.612429e+05 -1.754598e+05
## beta1 -1.736106e+05 -1.754598e+05 -2.079402e+05
## attr(,"time")
## Time difference of 0.1205029 secs
##
## --- END OF TRACE ---
##
##
## Time to Estimate Parameters:
## Time difference of 0.4151878 secs
##
## Title:
## GARCH Modelling
##
## Call:
## garchFit(formula = ~arma(1, 1) + garch(2, 1), data = d.series.name,
## include.mean = TRUE)
##
## Mean and Variance Equation:
## data ~ arma(1, 1) + garch(2, 1)
## <environment: 0x7fd1b9ab7d78>
## [data = d.series.name]
##
## Conditional Distribution:
## norm
##
## Coefficient(s):
## mu ar1 ma1 omega alpha1
## 8.8474e-04 -1.4871e-01 1.9984e-01 1.0041e-05 3.9450e-02
## alpha2 beta1
## 3.3402e-02 9.0814e-01
##
## Std. Errors:
## based on Hessian
##
## Error Analysis:
## Estimate Std. Error t value Pr(>|t|)
## mu 8.847e-04 4.451e-04 1.988 0.046835 *
## ar1 -1.487e-01 2.080e-01 -0.715 0.474662
## ma1 1.998e-01 2.058e-01 0.971 0.331439
## omega 1.004e-05 2.712e-06 3.702 0.000214 ***
## alpha1 3.945e-02 1.738e-02 2.270 0.023202 *
## alpha2 3.340e-02 2.103e-02 1.588 0.112285
## beta1 9.081e-01 1.456e-02 62.383 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Log Likelihood:
## 7695.869 normalized: 2.437716
##
## Description:
## Thu Jan 7 16:12:41 2016 by user:
##
##
## Standardised Residuals Tests:
## Statistic p-Value
## Jarque-Bera Test R Chi^2 158.6731 0
## Shapiro-Wilk Test R W 0.9921676 4.212096e-12
## Ljung-Box Test R Q(10) 12.27084 0.2673392
## Ljung-Box Test R Q(15) 24.79349 0.05278648
## Ljung-Box Test R Q(20) 27.02037 0.1346918
## Ljung-Box Test R^2 Q(10) 11.04974 0.3536558
## Ljung-Box Test R^2 Q(15) 14.87996 0.4600981
## Ljung-Box Test R^2 Q(20) 16.74909 0.6692009
## LM Arch Test R TR^2 12.86545 0.3788956
##
## Information Criterion Statistics:
## AIC BIC SIC HQIC
## -4.870997 -4.857566 -4.871007 -4.866178
